My previous blog on pressure bidding prompted another look at the so-called Law of Total Tricks and, especially, I fought the law by Mike Lawrence and Anders Wirgren.

One of the first things I realized twenty years ago when I first read about the "law" was of course that at best it is a rule of thumb. It is no more a true law (and perhaps even less so) than Bode's law. Some people, if I am to believe the L&W book, seem to believe that it is absolutely true, in the same way that certain fundamentalist religious people think that their "book" is literally true. I say this because Lawrence and Wirgren devote a large part of the book to debunking the myths of the LOTT. Would they bother if there weren't true believers?

Of course the "law" isn't literally true. Every bridge player knows that, including and especially Larry Cohen. And so do I. Yet, one of my bridge friends still chides me for quoting the law when making general statements about competitive bidding, as if I was one of the devoted followers, believing every word of the gospel.

Nevertheless, the "law" does, in a very general sense, show how the total number of tricks available (ours at our best trump suit plus theirs at their best trump suit) increase with the combined lengths of the two best trump suits (ours plus theirs). That's to say, on the whole, each additional trump (of ours) in one of our hands, or their trump in one of their hands, will result in an additional trick (either for us or for them). It doesn't state this as a categorical fact. It simply says that, in general, total tricks increases in step with total trumps.

Although it's never a true law, as mentioned above (in the majority of hands exact equality is the exception rather than the rule), it works best under the following conditions:

high card points are more or less evenly divided between the two opposing pairs (the usual range is quoted as 17-23 but this is of course an arbitrary boundary);

total trumps are nearer to 17/18 rather than the extremes of 14/21;

shortness and length are more or less in harmony (long suits beget short suits/voids);

you are willing to be off by one trick either way;

if you have a choice of trump suits of equal length, you choose the best one;

defense and declarer play at your table are perfect (double-dummy);

the layout doesn't contain too many short-suit honors, such as K, Qx, Jxx.

So, what use is the "law"? It can be useful when you have to make a competitive decision to bid on, pass or double and it is not completely obvious from bridge logic and experience what to do. This generally involves higher-level contracts, because an experienced player will be familiar with the lower level situations (should I bid 3♠ over their 3♥, for instance). Newer players can use it of course at all levels because they won't have developed the appropriate judgment yet.

As noted, it won't always be right. But bridge, especially matchpoints, is a game where we try to maximize our score in the long run without worrying too much about the occasional hand where things don't work out. For example, with no enemy bidding, no special avoidance requirements, and holding three small trumps in dummy (with outside entries) and AQT9x in our hand we will play low from dummy, playing the 9 if RHO plays low. Generally speaking, we expect to lose one trick only. But in fact, this favorable outcome will only occur 76% of the time. Do we feel hard done by if occasionally we lose two tricks? Of course not. Bridge is not normally a game of absolutes.

Now, you might be wondering what "long suits beget short suits/voids" was supposed to mean. What I mean by that is that as you get longer suits in your hand, you expect, or at least hope for, short suits to go with them, if not in your hand, then perhaps in partner's. For example, you pick up a 7-card suit. If the other suits are 2-2-2, this feels a little unnatural, and a bit of a disappointment, doesn't it? You'd be much less surprised by the 7-3-2-1 pattern. In fact, the 7-3-2-1 shape is three-and-one-half times more common than 7-2-2-2. And, as Lawrence and Wirgren tell us, it is really shortness rather than length that is most indicative of the number of tricks we can take. All things being equal, we'll take more tricks with a 7-3-2-1 hand than a 7-2-2-2 hand. But the "law" only takes into account the length of the trumps, in this case, presumably the seven-card suit. That's one of the obvious reasons why the law can't possibly be the gospel truth.

So, going back to my earlier question "what use is the law?", I do believe that it can help you decide what to do in a high-level competitive auction. Here's an example from a recent club game. You pick up in second seat, vulnerable versus not, ♠T7♥93 ♦KQT4 ♣97653. RHO passes, as do you, and LHO opens the proceedings with 2♠. Partner bids 4♣ (showing a good hand and at least 5-5 in hearts and clubs) and RHO bids 4♠. Now what? Let's try to do a "law" calculation. Given that LHO opened a weak two at favorable vulnerability in third seat, he probably has only five spades. I doubt if RHO has five spades with shape because he'd probably have jumped straight to 5♠. But he might have five spades without any shortness. It looks like we have a ten-card club fit and they have a nine-card spade fit so we're guessing 19, or possibly only 18 tricks. We don't have much in the way of points, but it does seem to be our hand, based on the auction so far, though perhaps not by a lot. If they can make 4♠ (-420), we could be -500 or even -800 in 5♣ so that doesn't look good. OTOH, if we can make 5♣ (600), they might be only -500 or -300 when doubled. We decide to pass smoothly (ah, there's the rub!) hoping that given partner's quasi-game-forcing bid, our pass will be considered forcing.

Partner comes in now with 5♥ which strongly suggests 6-5 in the round suits since he'd probably just double with the 5-5 he originally promised. RHO takes the push to 5♠ (perhaps he did have five spades after all) and we revise our idea of the hand now. It looks like they have 10 spades and we have 10 clubs with an 8-card heart fit. So I'm guessing we might have 20 total tricks. However, given that all our honors are in what appears to be a short suit in partner's hand (at most a doubleton), I'm going to be conservative and estimate 19 total tricks as before. So we decide to double expecting to gain 100, 300 or 500 as against (for 6♣) -800, -500, or -200. If we're wrong and there are 20 total tricks, we will be spectacularly wrong in the two extreme cases: they make 850 (pass would be best) or we could make 1370; but still doing fine in the middle (and perhaps more likely) cases: 100, 300 instead of -500, -200.

How did we do in practice? Both sides can take 10 tricks in their black suit, so it was right not to let them play 4♠. Their RHO made the all-too-common error of going to the well twice and falling down it the second time. We score +100 for about average (somewhat as we'd expect). However, there were no other pairs our way scoring 100 for 5♠X. Some pairs managed to set 5♠X two tricks but this must have been careless declarer play.

I think the law was helpful here, keeping us at average despite a difficult competitive board. It was difficult because a) our balanced and poorly fitting hand suggested fewer total tricks than there were; and b) the other side can make game on only 17 high-card points. For the full hand, look up board 18 from the Newton-Wellesley game on Christmas Eve. I was not playing, by the way, so all my thinking described above was fictional, but reasonable.

Friday, December 24, 2010

The general definition of a pressure bid is a uni-lateral and disruptive action by one player when he believes that the hand belongs to the other side. That's to say the player gets in and out quickly, using up as much room as is considered prudent. It's uni-lateral because, except under rare circumstances, his partner can be relied upon to do nothing likely to reduce the effectiveness of the bid. In other words, partner won't bid without extraordinarily good distribution. A pressure bid also aims to force the opponents to make the last guess (one of the goals of competitive auctions). Once in a while, the pressure bid will itself be doubled and this will be bad in 99% of all cases – you will have made the last guess! But in my experience this rarely, if ever, happens.

The usual reason to assume that partner won't kick an own goal later in the auction is that he's a passed hand and can be expected to follow the maxim that passed hands should never do anything questionable. These are the primary pressure situations. For example, white on red, ♠KJ8653♥97643 ♦9 ♣T where partner has passed as dealer and RHO passes. You know that LHO has a big hand and you want to do everything you can to deny him a nice comfortable auction. 3♠, or even possibly 4♠, is likely to be right here, exaggerating the length and quality of your spades. Sure, it can backfire, but if you and your partner are on the same wavelength, partner won't raise your preempt or attempt a sacrifice unless his hand is something like ♠Q942♥– ♦8542 ♣A9743, that's to say a highly offensively oriented hand for spades. On the other hand, you might make the following pressure bid: 2♠ with ♠KJ853♥Q93 ♦K92 ♣QT and fail to bid your game when partner shows up with ♠Q942♥3 ♦AJ542 ♣K94. But this bad outcome tends to be offset by the situations where the opposing declarer finesses into your two queens!

But what about extended pressure situations? Again, the vulnerability has to be favorable and it should appear that it's their hand. But we now allow partner to have made one bid, provided that the bid is relatively limited and descriptive. For example, a limited opening of 1♥ (precision, max of 15 hcp) or a 1♥ overcall. In contrast, some bids would not be appropriate partner actions for an extended pressure bid. For example, a minor suit opening, which may well be based on a balanced hand, or a two-suited bid which is sufficiently well-defined that partner should be able to make a good immediate guess.

Let's say that you have the following hand: ♠AT5♥KT962 ♦764 ♣AT and RHO deals and opens 1♣. You bid 1♥, and LHO makes a negative double. This is a classic extended pressure situation for partner if he has a heart fit and fewer than about 7 points. Most of the time, partner has a pretty good idea of what's in your hand: 5 (occasionally 6) hearts and somewhere between 8 and 15 points (more points are possible but of course unlikely). Your hand is also somewhat limited by the fact that both opponents are in the bidding. Let's say partner raises to 3♥. Does this guarantee four piece support? Not if the conditions are right for an (extended) pressure bid. Now let's suppose that RHO thinks for a bit and finally comes out with 3♠. You pass and LHO thinks for a bit and raises to 4♠ and it is back to you. You need to be fairly sure of at least 18 total tricks (and not 9 each side) to make a 5♥ sacrifice pay. Are you sure? The opponents almost surely have only eight spades between them and they are both probably near the minimum point-wise for their bidding. Even if we have 10 hearts between us, we have no shortness so 19 total tricks are probably not going to be available.

With this hand, I think you have a fairly clear nolo contendere. You have the worst possible shape for an overcall and partner declared that, in his opinion, 3♥ is as high as we should go, opposite a run-of-the-mill overcall. Let's hope that we can beat 4♠. If partner has pushed them into a lucky make with his pressure bid, then you will at least be winning the post-mortem.

But suppose your hand was instead ♠T53♥KQT962 ♦A76 ♣4. Yes, you might have bid 2♥ in the first round but with partner not yet having passed, you didn't want to preempt our chances of bidding game. If partner has something like ♠2♥AJ43 ♦JT98 ♣9764, it's very likely that they can make 4 or 5 spades while we are down 1 or 2 only at 5♥. We would want to sacrifice obviously.

But how do we know that partner hasn't made a pressure bid on ♠42♥AJ4 ♦JT98 ♣9762? It might still be right to sacrifice but it doesn't really look like it. How can we find out?

This is where the pressure bid control described by Robson and Segal is useful. Over 3♠, 3NT by your hand says to partner that you have a fine hand for sacrificing and if he does too, then go ahead and sacrifice over their 4♠, otherwise pass over 4♠ (but bid 4♥ over the likely double). Obviously, in the context of this auction, you can't possibly want to play 3NT. You need to have a hand that's as distributional as ♠T53♥KQT962 ♦A76 ♣4 to make this strategy safe: if they can't make game and 4♥ goes for 300 or worse, it won't be a good score! Of course, if your hand is two-suited, say ♠T3♥KQT62 ♦AQ642 ♣4 you will bid 4♦ over 3♠ and allow partner to evaluate his hand for a sacrifice (or even a make) in the context of a red two-suiter opposite.

Robson and Segal only describe the 3NT bid in the context of a primary pressure bid (i.e. where the potential raiser has initially passed). I've proposed extending its use, but it doesn't seem that anything could be lost by it since 3NT could never be a natural bid here.

Sunday, December 5, 2010

Of course, we knew that the Reisinger is considered by many to be the toughest event in the ACBL calendar. But what the hell, Kim and I decided to enter it anyway. The tricky part was persuading another pair of equally crazy masochists to join us. Fortunately, Matthew and Doug from Chicago were up for it. I had assumed that it would be a big event, somewhat similar to the Open BAM earlier in the week, maybe even bigger. But no, only 39 teams entered. The other experts entered the Swiss. But in our event, there were more world and national champions per square foot than any place I've ever been!

We were rubbish! We managed 10 wins out of 52. Yes, you read that right. We scored only slightly above 20%! In baseball, the "Mendoza line" for batting average is .200 but I generally think of the bridge Mendoza line as 30%. We thus achieved almost a super-Mendoza! We were, obviously, not among the 20 teams to advance to day two.

It's amazing that they allow palookas like us to enter this rather exclusive game, but they do. I could write up several stories from the day but many of them would simply demonstrate our ineptitude, or lack of experience at this level of bridge. Board-a-match scoring adds its own wrinkles to the game too. Here's a tricky decision I got wrong against Bill Gates and Sharon Osberg.

My hand was ♠KJ8653♥97643 ♦9 ♣T. Kim opened 1♦ and I bid 1♠ (we don't play weak jump shifts). Kim rebid 3NT and I made what turned out to be a good decision by bidding 4♥. I soon found myself in 4♠, Osberg led ♣A and the dummy that came down was surprisingly good: ♠AT♥A8 ♦AKQJ854 ♣52 (I might have opened 2♣ with this hand, although that could easily work out badly, using up too much room to describe the hand). Sharon continued with ♣K which I ruffed. I could see immediately that we might have missed a slam if the ♠Q was on side. Would they be likely to be in 6♠ at the other table? Gates doesn't play with World Champions on his team but they are very good players. It seemed to me that, missing a key card and the ♠Q, they would likely stop in 5♠. In any case if slam was making and they were in it, we'd already lost the board. What would be the best way to make 5♠? Assuming our teammates didn't lead a heart, my counterpart would likely play off the two top spades and start on the diamonds, guaranteeing the contract if the spades were 3-2 and making an overtrick if the Q was doubleton. Of course I had a slight luxury in that I could afford to finesse the Q provided that Sharon didn't switch to hearts if she could win it. So, by finessing against the Q, I would win if Gates had it. She hadn't played a heart yet and maybe she wouldn't even then, I deluded myself. As it was, she had the ♠Qxx and was keen to demonstrate to Gates the "Merrimack coup" by sacrificing her ♥K. Curtains for me. I had gambled and lost: down 2.

I think I should have taken the money by making my game on the grounds that if 6 was making and they were in it, we'd lose anyway. Playing my way gave a 34% chance of making 6 and would make exactly or be down 1 or 2 (depending on the diamond split) if RHO had ♠Qxxx (11%). But 55% of the time I was down 2 for sure. Playing to make would result in +450 68% of the time. I didn't guess sufficiently accurately what was happening at the other table.

What did happen? Our opponents played in 3NT and our teammates led a club (the good news). But (bad news) the clubs split 5-5 so that contract was down only 1 and we lost the board. As it turned out, playing to make the contract (as would be appropriate in an IMP team game) would have worked beautifully.

Here's an example of the kind of play you don't experience too often at the local bridge club.

Kim was in 4♠ with Norwegian World Champions Tor Helness on her left and Geir Helgemo on her right. The heart suit was AQT3 in dummy and J762 in hand. Kim led low to the T and it held. She now had two heart tricks, one ruff already in and the ♣A for sure. Six more trumps on a complete cross-ruff would provide an over trick, assuming one trump gets overruffed at the end. After returning to the ♣A, she led another low heart. What if Helgemo was out of hearts and ruffed in returning a trump? That would mean only 9 tricks. So she repeated the "marked" finesse, losing to the K. The contract could no longer be made. Helgemo's original holding? ♥Kx! Just one more lost board? Yes, but in fact, Helgemo's decision to duck his K was going to allow Kim to make 11 tricks if she plays all out and finesses the ♣Q in her hand. So, while it was a brave and, for us, unusual play, it turns out that the guy some believe is the single best player in the world (but ranked #11 by the WBF) actually made an error. But it induced a matching error from our side and in the end worked very well. Our two hands were ♠A983♥J762 ♦– ♣AQT63 (declarer) and ♠Q765♥AQT3 ♦T852 ♣8 (dummy).

Other notables that we faced at our table: Gitelman/Moss, Levin/Weinstein, Pepsi/Lev, Doub/Wildavsky, Cheek/Grue, Koneru/Chorush, Bocchi/Ferraro and other well-known players.

If we make it to Seattle next year as we hope, I think I'm going to skip the Reisinger and try the Swiss. There's typically only a few World Champions playing in that event and many more teams overall. Still tough to qualify but at least within the realms of possibility.

Thursday, December 2, 2010

A welcome break from the intensity (and elimination) of the (open) Blue Ribbons came in the A/X Swiss. Our first lucky break was meeting up with Saul and Ed buying a pairs entry. We decided to team up for the Swiss.

There were many good teams among the 40 entrants, many of which had like us been kicked out of the Blues. We were using the 30 victory point scale which emphasizes winning above all else. You get 15 for a tie but only 12 for a 1 imp loss. This is Bobby Wolff's scale and I think it really is better than the 20 point scale. We won the first match handily but got the flip side of the coin when we somewhat surprisingly lost the second match. Two more wins put us in 6th place for the dinner break which helped make the meal pleasant and relaxing. Incidentally, Kathy and her partner were with us and they were lying 2nd in the B/C/D Swiss.

We met a team of Polish internationals after dinner and lost fairly badly. Then we went up against Billy Miller's team. The first six boards were uneventful but I had a feeling that we were losing the match. We were but only by one (but as mentioned that would have gained us only 12 VPs). I picked up the following beautiful hand in fourth seat, vulnerable against not: ♠AKQJ763♥7 ♦AJ972 ♣ –. This was going to generate some action, I thought :) Kim somewhat surprisingly opened 1NT (15-17) and this looked like a fairly easy hand in our methods (e.g. 1NT 2♥ 2♠ 5♣ ...) where 5♣ would be exclusion keycard Blackwood. Needless to say, the opponents were not going to make it easy at those colors. It went 3♥ by Miller and I had to decide what to do. We play that 4♦or 4♥ are transfers providing that they are jumps or cuebids. In any case, 4♥ would be forcing so that was my call (Kim alerting appropriately). LHO put in 5♥ and Kim, bless her, accepted the transfer with 5♠. Now it was up to me. I didn't know what else was in her hand but the one thing I needed her to have was the ♥A obviously. I therefore bid 6♥. Now she bid 6NT. This worried me a bit (what if she has only KQ or Kx of hearts?). But I wasn't sure 6NT would yield even twelve tricks opposite my hand so I bid 7♠. There was always the possibility, admittedly slight, that Miller wouldn't lead the A even if he had it, thinking my sequence showed a void. Anyway, Miller led a trump and Kim scored up 7♠ and we won 13 imps, giving us 25 VPs instead of the 12 we would otherwise get. Kim's hand was ♠T92♥AQ ♦K6 ♣AQT754.

We won the last two matches with small but significant scores and ended up in 8th overall, 2nd in X. Kathy's team ended 4th in the other event. So, it was a good day. The Orlando bridge gods smiled on us at last :)